“KWARC was!”

After reading the book How to solve it by Polya [Pol73], I decided to analyze different ways of problem solving based on how my colleagues and students (altogether 10 volunteers) proved the following simple lemmas: (1) For all prime numbers p≥5 prove that z=p2-1 is divisible by 24 and (2) Proof that the center of gravity of a polygon equals the average of all points of the polygon. Although no representative survey was carried out, the case study brought up some interesting findings: For (1), some person wrote a lot of explanatory text for almost every step of their proof; while others skipped several steps they found obvious. The level of formality varied among the test persons: some wrote their proofs very close to a form that could be verified by e.g. theorem provers, while others stick to a rather informal writing of their proofs. Moreover, the test persons took different approaches of how to proof the lemma: Some could easily write down a formal proof, while others started with examples and counter examples to get a better idea of how to solve the given problem. For (2), some test persons used drawings to get a better idea whether they had to proof or refute the given geometric problem.